Find the value of a6-1-a3-given that a2-1-a-2

Given, a^2 1/a = 2 Cubing on both sides, we get, a^2 1/a^3=8 [a^6 1 3a^2 (a^2 1)]/a^3=8 a^6 1/a^3 3a^2 1/a=8 a^6 1/a^3=8+3(a^2 1)/a=8 + 3× 2 = 14. ...

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Find the value of $\frac{a^{6} - 1}{a^{3}}$ ,given that $\frac{a^{2} - 1}{a} = 2$ .

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Solution

$G i v e n, \frac{a^{2} - 1}{a} = 2$
Cubing on both sides, we get,
$\frac{a^{2} - 1}{a^{3}} = 8 \frac{[a^{6} - 1 - 3 a^{2} (a^{2} - 1)]}{a^{3}} = 8 \frac{a^{6} - 1}{a^{3}} - 3 \frac{a^{2} - 1}{a} = 8 \frac{a^{6} - 1}{a^{3}} = 8 + \frac{3 (a^{2} - 1)}{a} = 8 + 3 \times 2 = 14$ .

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Find the value of $\frac{a^{6} - 1}{a^{3}}$ given that $\frac{a^{2} - 1}{a} = 2$

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\frac{a^{2} - 1}{a} = 2

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a_{1}, a_{2}, a_{3}, \dots

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a_{1} + a_{2} + a_{3} + \dots \dots + a_{98} = 137

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Find the value of a6−1a3,given that a2−1a=2.

Given, a2−1a=2 Cubing on both sides, we get, a2−1a3=8[a6−1−3a2(a2−1)]a3=8a6−1a3−3a2−1a=8a6−1a3=8+3(a2−1)a=8+3×2=14.

Find the value of $\frac{a^{6} - 1}{a^{3}}$ ,given that $\frac{a^{2} - 1}{a} = 2$ .

$G i v e n, \frac{a^{2} - 1}{a} = 2$
Cubing on both sides, we get,
$\frac{a^{2} - 1}{a^{3}} = 8 \frac{[a^{6} - 1 - 3 a^{2} (a^{2} - 1)]}{a^{3}} = 8 \frac{a^{6} - 1}{a^{3}} - 3 \frac{a^{2} - 1}{a} = 8 \frac{a^{6} - 1}{a^{3}} = 8 + \frac{3 (a^{2} - 1)}{a} = 8 + 3 \times 2 = 14$ .